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We propose the concept of local-k farsighted consistent network for analysing network formation games where players only consider a limited number of feasible networks. A network g is said to be local-k farsightedly consistent if, for any network g' within the distance-k neighbourhood of g, either g is not defeated by g' , or g defeats g' . We show that if the utility function is (componentwise) egalitarian or satisfies reversibility or excludes externalities across components, then local-k farsightedness is more likely to be a good proxy for what would happen when players have full knowledge of all feasible networks.

We analyze the formation of R&D alliances and market sharing (MS) agreements by which firms commit not to enter in each other’s territory in oligopolistic markets. We show that R&D alliance structures are stable only in the presence of MS agreements. Thus, long lasting R&D alliances could signal the existence of some MS agreement in the industry. We characterize the set of stable symmetric pairs of coalition structures with identical R&D and MS structure. In addition, we show the stability of a class of asymmetric pairs of coalition structures where the most efficient firms form both an R&D and a MS agreement while the other firms do not form any MS agreement but form two smaller R&D alliances. Even though MS agreements are detrimental for consumers, we show that stable cooperation in terms of R&D is yet a better outcome for consumers than no cooperation at all.

We study the formation of R&D networks when firms can be either myopic or farsighted.Stability leads to R&D networks consisting of either asymmetric components or nearly symmetric components. Farsighted firms have in average more collaborations but myopic firms can be central for spreading the innovation. We introduce yes-firms that form links subject to the constraint of non-negative profits. Yes-firms stabilize R&D networks that maximize social welfare. Finally, the evolution of R&D networks shows that nearly symmetric R&D networks will be rapidly dismantled, socially optimal R&D networks will persist many periods, while asymmetric R&D networks will persist forever.

Individuals are embedded in a network of relationships and they can be victims, bystanders, or perpetrators of bullying and harassment. Each individual decides non-cooperatively how much effort to exert in preventing misbehavior. Each indi- vidual’s optimal effort depends on the contextual effect, the social multiplier effect and the social conformity effect. We characterize the Nash equilibrium and we derive an inter-centrality measure for finding the key player who once isolated increases the most the aggregate effort. An individual is more likely to be the key player if she is influencing many other individuals, she is exerting a low effort because of her characteristics, and her neighbors are strongly influenced by her. The key player policy increases substantially the aggregate effort and the targeted player should never be selected randomly. The key player is likely to remain the key player in presence of social workers except if she is becoming much less influential due to her closeness to social workers. Finally, we consider alternative policies (e.g. training bystanders for helping victims) and compare them to the policy of isolating the key player.

We reconsider de Marti and Zenou (2017) model of friendship network formation where individuals belong to two different communities and costs of forming links depend on community memberships. Many inefficient friendship networks such as segregation can arise when all individuals are myopic. Once there are myopic and farsighted individuals in both communities, we show that if there are enough farsighted individuals in the dominant community relatively to the number of individuals in the small community, then the friendship network where the smaller community ends up being assimilated into the dominant community is likely to emerge and is strongly and Pareto efficient. Moreover, this friendship network Pareto dominates the complete segregation network.

We propose the notion of coalition-proof stability for predicting the networks that could emerge when group deviations are allowed. A network is coalition-proof stable if there exists no coalition which has a credible group deviation. A coalition is said to have a credible group deviation if there is a profitable group deviation to some network and there is no subcoalition of the deviating players which has a subsequent credible group deviation. Coalition-proof stability is a coarsening of strong stability. We emphasize the importance of coalition-proof stability by considering four models where a strongly stable network fails to exist while a coalition-proof stable network does exist. We provide an easy to verify condition for the existence of a coalition-proof stable network while a strongly stable network may not exist. There is no relationship between the set of coalition-proof stable networks and the set of networks induced by a coalition-proof Nash equilibrium of Myerson’s linking game.

We propose the notion of myopic-farsighted absorbing set to determine the networks that emerge in the long run when some players are myopic while others are farsighted. A set of networks is a myopic-farsighted absorbing set if (No External Deviation) there is no myopic-farsighted improving path from networks within the set to some networks outside the set, (External Stability) there is a myopic-farsighted improving path from any network outside the set to some network within the set, and (Minimality) there is no proper subset satisfying No External Deviation and External Stability. Contrary to the notion of myopic-farsighted stable set, we show that a myopic-farsighted absorbing set always exists. We partially characterize the myopic-farsighted absorbing sets and we provide sufficient conditions for the equivalence between a myopic-farsighted absorbing set and a myopic-farsighted stable set. We also introduce and fully characterize the notion of proper myopic-farsighted absorbing set that refines the concept of myopic-farsighted absorbing set by selecting the more absorbing networks. Finally, we consider a threshold game that illustrates the role of the relative number of farsighted and myopic players for reaching efficiency.

We adopt the horizon-K farsighted set of Herings, Mauleon and Vannetelbosch (2019) to study the R &D networks that will emerge in the long run when firms are neither myopic nor fully farsighted but have some limited degree of farsightedness. We find that a singleton set consisting of a pairwise stable network is a horizon-K farsighted set for any degree of farsightedness K≥2. That is, each R &D network consisting of two components of nearly equal size satisfies both horizon-K deterrence of external deviations and horizon-K external stability for K≥2. On the contrary, each R &D network consisting of two components with the largest one comprising three-quarters of firms, predicted when all firms are fully farsighted, violates horizon-K deterrence of external deviations. Thus, when firms are homogeneous in their degree of farsightedness, pairwise stable R &D networks consisting of two components of nearly equal size are robust to limited farsightedness.

We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other individuals but also about how a mediator is going to solve conflicts of interest. The set of socially rationalizable outcomes with mediation is shown to be non-empty for all social environments, and it can be computed by an iterative reduction procedure. We show that social rationalizability with mediation does not necessarily satisfy coalitional rationality when the number of coalition members is greater than two.

We study a coordination game on a fixed connected network where players have to choose between two projects. Some players are moderate (i.e. they are ex-ante indifferent between both projects) while others are stubborn (i.e. they always choose the same project). Benefits for moderate players are increasing in the number of neighbors who choose the same project. In addition, players are either farsighted or myopic. Farsighted players anticipate the reactions of others while myopic players do not. We show that, when all players are farsighted, full coordination among the moderate players is reached except if there are stubborn players for both projects. When the population is mixed, the set of stable strategy profiles is a refinement of the set of Nash equilibrium strategy profiles. In fact, turning myopic players into farsighted ones eliminates gradually the inefficient Nash equilibria. Finally, we consider a social planner who can improve coordination by means of two policy instruments: adding links to the network (socialization) and/or turning myopic players into farsighted ones (education).